Mathematical Sciences: Interacting Particle Systems

该项目包括四个专题。 第一部分涉及 无限粒子系统的近似 有限的系统，因为时间和系统的大小都倾向于 到无穷远 这些结果特别重要， 观点的无限粒子系统作为模型， 各种实际问题。 第二个问题涉及到大 非相互作用随机Poisson系统的偏差率 走路. 第三个话题可以说是传播 幸存粒子遵循分支过程模型。 的 相应的理论问题探讨了聚类和 分支随机游动的合并行为。 最后一个领域 相对来说，研究还没有被探索过。 多类型系统 具有非吸引性、非加性状态空间， 在流行病或化学反应中自然产生。 这样的系统 将展现出新奇有趣的现象

The project consists of four topics. The first deals with the approximation of the infinite particle systems by large finite systems as both the time and the size of the system tend to infinity. These results are particularly important from the point of view of the infinite particle systems as models for various practical problems. The second topic concerns the large deviation rate in a Poisson system of noninteracting random walks. The third topic can be described as the spread of the surviving particles following branching process models. The corresponding theoretical questions explore the clustering and coalescing behavior of the branching random walks. The last area of inquiry is relatively unexplored as yet. Multitype systems with non-attractive, non-additive state space, without duals arise naturally in epidemics or chemical reactions. Such systems are expected to exhibit new and interesting phenomena.